A cipher is defined over the spaces of: All Keys, \(\mathscr{K}\) All Messages, \(\mathscr{M}\) All Cipher texts, \(\mathscr{C}\) Cipher (defined as a triple, \((\mathscr{K}, \mathscr{M}, \mathscr{C})\)) as a pair of algorithms \((\mathbf{E}, \mathbf{D})\) where \(\mathbf{E}\) represents the encryption algorithm and \(\mathbf{D}\) represents the decryption algorithm. \begin{equation} \mathbf{E}: \mathscr{K} \times \mathscr{M} \rightarrow \mathscr{C} \end{equation} and \begin{equation} \mathbf{D}: \mathscr{K} \times \mathscr{C} \rightarrow \mathscr{M} \end{equation} Such that: \begin{equation} \forall m \in \mathscr{M}, k \in \mathscr{K}: \mathbf{D}(k, \mathbf{E}(k, m)) = m \end{equation} ...

Distribution Vector

Cryptography Probability

A vector with non-negative components (representing specific probabilities) which add up to one e.g. \begin{equation} (P(x_{0}), P(x_{1}),…,P(x_{n})) \end{equation} Also known as: Stochastic Vector

Uniform Distribution

Math Probability Cryptography

\begin{equation} x \in U:P(x) = \frac{1}{|U|} \end{equation} Where \(|U|\) is the size of the universe (set). In Probability Theory, a uniform distribution assigns an equal probability to each element of a given set.